Ben decided to paint some of the rooms at his 17-room inn, Ben's Place. He discovered he needed $\frac{2}{5}$ of a can of paint per room. If Ben had 6 cans of paint, how many rooms could he paint?
We can divide the cans of paint (6) by the paint needed per room ( $\frac{2}{5}$ of a can) to find out how many rooms Ben could paint. $ \dfrac{{6 \text{ cans of paint}}} {{\dfrac{2}{5} \text{ can per room}}} = {\text{ rooms}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{2}{5} \text{ can per room}}$ is ${\dfrac{5}{2} \text{ rooms per can}}$ $ {6\text{ cans of paint}} \times {\dfrac{5}{2} \text{ rooms per can}} = {\text{ rooms}} $ ${\dfrac{30}{2}\text{ rooms}} = 15\text{ rooms}$ Ben could paint 15 rooms.